Real Numbers

Rational numbers can be expressed as a fraction of two integers and have either terminating or repeating decimal expansions. Irrational numbers cannot be expressed as fractions and have non-terminating, non-recurring decimals.

By expressing each number in terms of its prime factors, we can identify the highest power of each prime factor present in the numbers. Multiplying these factors gives the LCM.

Certain square roots cannot be expressed as a fraction because their decimal expansions are non-terminating and non-repeating. The proof often involves assuming the number is rational and reaching a contradiction.

Euclid’s Division Lemma allows us to systematically divide two numbers, using remainders to progressively reduce the numbers until we reach the HCF. This method is efficient and widely used in number theory.

Yes, imaginary numbers, like the square root of -1 (denoted as i), are not real numbers. They form part of the complex numbers when combined with real numbers.

Zero is the additive identity in real numbers, meaning [...]

Yes, real numbers can be both positive and negative, [...]

Rational numbers can be expressed as a fraction with [...]

A real number can be any rational or irrational [...]